Can autoencoders be used for supervised learning?
One such paper I know of and which I implemented is Semi-Supervised Learning using Ladder Networks . I quote here their description of the model:


  Our approach follows Valpola (2015), who proposed a Ladder network where the auxiliary task is
  to denoise representations at every level of the model.  The model structure is an autoencoder with
  skip connections from the encoder to decoder and the learning task is similar to that in denoising
  autoencoders but applied to every layer, not just the inputs. The skip connections relieve the pressure
  to represent details in the higher layers of the model because,  through the skip connections, the decoder can recover any details discarded by the encoder.


For further explanations on the architecture check Deconstructing the Ladder Network Architecture by Yoshua Bengio.